弹性力学应力状态理论求解器开发及应用研究

论文基于吴家龙教授编著的《弹性力学》教材内容和课程"三难"特点,以应力状态理论部分常见题型求解任意微分斜面应力矢量、正应力、切应力、主应力和应力主方向及最大切应力为例,应用Matlab-GUI模块编制应力状态理论求解器,通过界面物理参数输入和结果显示过程,再现弹性力学求解思维,验证学生数理求解结论;把繁琐抽象的力学公式和微分斜面结果进行图形可视化,使学生的抽象思维和力学思维得到兼容;通过弹性力学应力状态理论求解器开发及应用,可为学生力学学习及力学同行教学提供借鉴。

DEVELOPMENT AND APPLICATION OF STRESS STATE THEORY SOLVER FOR ELASTICITY

Based on the textbook Elasticity by Wu Jialong, and the "trilemma" characteristics of the course,taking the common questions in the stress state theory as examples, the stress vector, the normal stress, the shear stress, the principal stress, the principal direction of the applied force and the maximum shear stress on any differential inclined plane are included. The Matlab–GUI module is used to compile the stress state theory solver, By processing the inputting physical parameters and displaying results, the thinking process of the elasticity is reproduced and the mathematical solution is verified, the complex abstract mechanical formulas and the differential slope results are clarified in graphic visualization, so that the students’ abstract thinking and mechanical thinking are linked. The stress state theory solver of elasticity can provide a reference for students’ mechanics learning and for mechanics teaching.